One of the exciting developments in observational cosmology over the last few years has been the ability to extend studies of element abundances from the local universe to high redshifts. Thanks largely to the new opportunities offered by the Keck telescopes, the Very Large Telescope facility at the European Southern Observatory, and most recently the Subaru telescope, we find ourselves in the exciting position of being able, for the first time, to detect and measure a wide range of chemical elements directly in stars, H II regions, cool interstellar gas and hot intergalactic medium, all observed when the universe was only ~ 1/15 of its present age. Our simple-minded hope is that, by moving back to a time when the universe was young, clues to the nature, location, and epoch of the first generations of stars may be easier to interpret than in the relics left today, some 12 Gyrs later. Furthermore, the metallicities of different structures in the universe and their evolution with redshift are key factors to be considered in our attempts to track the progress of galaxy formation through the cosmic ages.
In the last few years, work on chemical abundances at high redshifts has concentrated on four main components of the young universe: Active Galactic Nuclei (AGN), that is quasars (QSOs) and Seyfert galaxies; two classes of QSO absorption lines, the damped Ly systems (DLAs) and the Ly forest; and on galaxies detected directly via their starlight, also referred to as Lyman break galaxies. In these series of lectures I will review results pertaining to the last three; for abundance determinations in the emission line regions of AGN and associated absorbers I refer the interested reader to the excellent recent overview by Hamann & Ferland (1999).